Question

Can you help with this question? I'm not sure if the black highlighted choice is right. The question is positive so would it be answer D

Answer 1

Given the following function:

$f(x)=\frac{5x}{\sqrt{3x^2-12}}$

We will find the domain of the function f(x)

As shown, it is a rational function and there is a square root in the denominator

So, the domain is all real numbers except the values that make the denominator zero or negative

So, we need to solve the following inequality:

$3x^2-12>0$

We will solve the inequality as follows:

$\begin{gathered} 3x^2>12 \\ x^2>\frac{12}{3} \\ x^2>4 \\ x>2,or,x<-2 \end{gathered}$

So, the answer will be

D. all real numbers such that x > 2, x < -2